and therefore the \([p]\) -mapping on
\(\mathfrak {m}_2^\lambda (p)\)  is \(p\) -semilinear (see also [1]}). From this we get that if
\(g=\sum \alpha _k e_k\in \mathfrak {m}_2^\lambda (p)\) , then
\( g^{[p]}=\left(\sum _{k=1}^p \alpha _k^p\lambda _k \right) e_p.\) 
